Average Error: 10.5 → 1.0
Time: 11.8s
Precision: 64
\[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
↓
\[x + \left(\left(y - z\right) \cdot \frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{t}}{\sqrt[3]{a - z}}\]
x + \frac{\left(y - z\right) \cdot t}{a - z}
↓
x + \left(\left(y - z\right) \cdot \frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{t}}{\sqrt[3]{a - z}}
double f(double x, double y, double z, double t, double a) {
        double r455354 = x;
        double r455355 = y;
        double r455356 = z;
        double r455357 = r455355 - r455356;
        double r455358 = t;
        double r455359 = r455357 * r455358;
        double r455360 = a;
        double r455361 = r455360 - r455356;
        double r455362 = r455359 / r455361;
        double r455363 = r455354 + r455362;
        return r455363;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r455364 = x;
        double r455365 = y;
        double r455366 = z;
        double r455367 = r455365 - r455366;
        double r455368 = t;
        double r455369 = cbrt(r455368);
        double r455370 = r455369 * r455369;
        double r455371 = a;
        double r455372 = r455371 - r455366;
        double r455373 = cbrt(r455372);
        double r455374 = r455373 * r455373;
        double r455375 = r455370 / r455374;
        double r455376 = r455367 * r455375;
        double r455377 = r455369 / r455373;
        double r455378 = r455376 * r455377;
        double r455379 = r455364 + r455378;
        return r455379;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.5
Target0.7
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;t \lt -1.068297449017406694366747246993994850729 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t \lt 3.911094988758637497591020599238553861375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

  1. Initial program 10.5

    \[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity10.5

    \[\leadsto x + \frac{\left(y - z\right) \cdot t}{\color{blue}{1 \cdot \left(a - z\right)}}\]

  4. Applied times-frac3.3

    \[\leadsto x + \color{blue}{\frac{y - z}{1} \cdot \frac{t}{a - z}}\]

  5. Simplified3.3

    \[\leadsto x + \color{blue}{\left(y - z\right)} \cdot \frac{t}{a - z}\]
  6. Using strategy rm

  7. Applied add-cube-cbrt3.7

    \[\leadsto x + \left(y - z\right) \cdot \frac{t}{\color{blue}{\left(\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}\right) \cdot \sqrt[3]{a - z}}}\]

  8. Applied add-cube-cbrt3.8

    \[\leadsto x + \left(y - z\right) \cdot \frac{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}}{\left(\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}\right) \cdot \sqrt[3]{a - z}}\]

  9. Applied times-frac3.8

    \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\left(\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{\sqrt[3]{t}}{\sqrt[3]{a - z}}\right)}\]

  10. Applied associate-*r*1.0

    \[\leadsto x + \color{blue}{\left(\left(y - z\right) \cdot \frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{t}}{\sqrt[3]{a - z}}}\]

  11. Final simplification1.0

    \[\leadsto x + \left(\left(y - z\right) \cdot \frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{t}}{\sqrt[3]{a - z}}\]

Reproduce

herbie shell --seed 2019323 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (if (< t -1.0682974490174067e-39) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t))))

  (+ x (/ (* (- y z) t) (- a z))))